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Edge resolvability of crystal cubic carbon structure

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Abstract

Graph theory plays an important role for modelling and designing chemical structures and complex networks. Chemical graph theory is commonly used to analyse and comprehend chemical structures and networks, as well as their features. In graph theory, a chemical structure can be represented by vertices and edges where vertices denote atoms and edges denote molecular bonds. The concept of resolvability parameters for a graph G= (V, E) is a relatively new advanced field in which the complete structure is built so that each vertex (atom) or edge (bond) represents a distinct position. It plays a very prominent role in analysing the overall symmetry and structural properties of new chemical compounds. The goal of this study is to employ chemical graph theory to determine some graph-related parameters related to chemical graphs of hypothesised carbon allotrope. In this article, we study the resolvability parameters, i.e. edge resolvability of the chemical graph of the crystal structure of cubic carbon (CCS(n)).

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Funding

The work of Sahil Sharma is supported by Shri Mata Vaishno Devi University (ref no SMVDU / R &D / 19 / 2661-65).

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Authors and Affiliations

  1. School of Mathematics, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, 182320, India

    Sahil Sharma, Vijay Kumar Bhat & Sohan Lal

Authors
  1. Sahil Sharma
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  2. Vijay Kumar Bhat
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  3. Sohan Lal
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Contributions

Concept and final draft by SS and VKB; figures and graphs were prepared by SS and SL; supervision and editing by VKB, and all authors reviewed the final draft.

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Correspondence to Vijay Kumar Bhat.

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The authors disclose that they have no competing interests.

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Novelty statement

The edge resolvability of various well-known graphs has recently been computed. For instance, convex polytopes, web graphs, circulant graphs, certain chemical structures, and so on. In chemistry, one of the most important problems is to represent a series of chemical compounds mathematically so that each component has its representation. Graph invariants play an important role to analyse the abstract structures of chemical graphs. But there are still some chemical graphs for which the vertex and edge resolvability have not been found yet, one such compound is crystal cubic carbon structure CCS(n). Therefore, in this article, we compute the edge resolvability of CCS(n), for \(n\ge 1\) and see that \(edim(CCS(n)) = dim(CCS(n))\).

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Sharma, S., Bhat, V.K. & Lal, S. Edge resolvability of crystal cubic carbon structure. Theor Chem Acc 142, 24 (2023). https://doi.org/10.1007/s00214-023-02964-3

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